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The number of vehicle-borne explosive attacks last month was just one, resulting in six casualties, as opposed to 42 attacks and 186 victims in July last year.

With violence down and Iraqi Security Forces taking on more day-to-day security details, Americans are able to more fully mine the other components of their counterinsurgency plan.

Maj. Greene´s battalion operates in Adhamiya, a district close to Sadr City, the former stronghold of Mr. al-Sadr and his Mahdi militia.

Sadr City came under Iraqi army control in late May when Mr. al-Sadr agreed to a cease-fire with the Iraqi government. Iraqi troops entered its main northern sector and now control it. U.S. and Iraqi forces earlier took control of Sadr City´s southern districts.

Sgt. 1st Class Robert Rollheiser and other combat engineers in Echo Company recalled the constant sniper fire and rocket attacks in April and May while finding and destroying scores of bombs planted along a key thoroughfare where U.S. forces were erecting a wall between southern and northern Sadr City.

Today, route clearance is an Iraqi affair while the U.S. engineers visit neighborhoods, knocking on doors and combing markets to make friends while also seeking out extremist holdouts or infiltrators.

“We´re going back the market in Muhalla [neighborhood] 343 and stir things up a bit,” Sgt. Rollheiser said during a pre-mission brief at Combat Operations Post Callahan.

“We know the leaders of [Jaish al-Mahdi] and the special groups have run, but there are others left who are coming into our district. We can´t catch them all. We can´t kill them all. But we can make their lives … difficult.”

The market that the Echo Company patrolled was a crowded and sprawling mix of single-story shops and open-air stalls selling food, sundries and gadgets amid piles of garbage and pools of sewer water. The mission was to glad-hand shoppers, assess their mood on security and livability issues, and gain information on terrorists.

Despite the change in U.S. tactics, Sgt. Rollheiser said he has begun to suspect that extremists from Sadr City are infiltrating the area to escape Iraqi army mop-up operations. People who earlier would approach and chat openly with the Americans have become more reserved and hesitant, he said. Sgt. Rollheiser suspects they are afraid of who might be watching.

While Echo Company engineers passed out fliers appealing for information, Sgt. Rollheiser made a great show of peering at a photograph and then looking hard at shoppers´ faces or showing the photograph and asking questions about the four men in it.

“Ever see these guys?” he asked through an interpreter. “They´re criminals; they blow up children. I don´t like people who blow up children. Have you seen them?”

Sgt. Rollheiser obtained the photograph during a raid on the home of an extremist gunman just a couple of blocks from the market.

The home had been disclosed by a Sons of Iraq volunteer neighborhood guard.

The picture showed four extremists relaxing outside a local hookah shop. Sgt. Rollheiser knew that the odds of someone in the market knowing one of the men and telling where they were last seen were slim, but holding the picture and then scanning faces in the crowd would get out the word that the Americans were looking for specific suspects, not conducting indiscriminate raids. Pleasantries as well as pressure are now the name of the game.